Question

What is the completely factored form of 25x4 – 16y2?

Answer 1

Das is difference of 2 perfect squares
remember
a^2-b^2=(a-b)(a+b)

so
25x^4=(5x^2)^2
16y^2=(4y^2)

(5x^2)^2-(4y)^2=(5x^2-4y)(5x+4y)
cannot be factored further

Answer 2

Answer:

$(5x^{2} + 4y),(5x^{2} - 4y)$

Step-by-step explanation:

Given  : $25x^{4} - 16y^{2}$.

To find : What is the completely factored form .

Solution : We have given  $25x^{4} - 16y^{2}$.

We can write it as

$(5x^{2})^{2} - (4y)^{2}$

Using the identity $a^{2} - b^{2} = (a+b) (a-b)$.

Here, a = $(5x^{2})$ , b = $(4y)$.

Then  ,

$(5x^{2})^{2} - (4y)^{2}$ = $(5x^{2} + 4y) , (5x^{2} - 4y)$

Therefore, $(5x^{2} + 4y),(5x^{2} - 4y)$